Upon receiving my bike from United Airlines, the front of my bike box was ripped off and the box itself was twisted, so it appears it was placed under an extremely high load.
Upon building my bike back up, the frame and fork are scratched and the front hydraulic brake housing is slightly kinked. The brakes work fine, but I would probably feel best if the housing were replaced. I didn't check if the frame was bent yet or other details as that takes a bit more effort. That will be my plan for today.
It took about an hour to get the luggage off the plane because a cargo door would not open. I am suspecting that the bike box was not properly stored or somehow came loose in the cargo area and upon landing, found itself jammed up against the cargo door. When trying to open the cargo door, the bike box was damaged. That is just my guess with the information that was provided. The damage pattern looks like a large sheer force was exerted on it, the kind of force that would exist from opening a door. I thought all luggage had to be properly secured in the cargo area since that would affect the plane's CG.
Upon receiving my bike, I immediately filed a claim and United reminded me that bikes are not covered unless they're in a hard case. I will report the damage that I found as well as check if the frame is perhaps bent or damaged by looking for stresses to the paint job, cracks in welds, and if the front and rear wheel track together.
What else should I do or expect?
EDIT:
I will attach pictures soon when my computer cooperates. The bike frame is steel and the fork is carbon. All the comments make sense, this is more of a legal / travel issue with airlines. My bike is insured, but before I go that route, I would take it to a bike shop to have them inspect it.